One way to get your milk without all the carbs is to mix 1/2 cup of heavy cream (also known as whipping cream) with 1/2 cup water. You get milk for about 3 grams of carb per cup.
I do have to wonder about a hidden intolerance or allergy to milk, though, since you're craving it so strongly. Many people crave the very things that they should be avoiding because their bodies can't handle it.
While the glycemic value of milk may be low, it's the carbs that matter for now (at least if you're following Atkins), so I wouldn't advise you to start drinking a liter of milk a day at this point.